3x^2+231=-54x

Solution for 3x^2+231=-54x equation:

3x^2+231=-54x

We move all terms to the left:

3x^2+231-(-54x)=0

We get rid of parentheses

3x^2+54x+231=0

a = 3; b = 54; c = +231;
Δ = b2-4ac
Δ = 542-4·3·231
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-12}{2*3}=\frac{-66}{6}
=-11
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+12}{2*3}=\frac{-42}{6}
=-7
$